In a city, 40.1% of the adults are illiterate while
85.1% of the children are literate. If the ratio of the
adults to that of the children is 2:3, then what percent
of the population is literate?
Solution
Let total population be $100$ (as given).
Ratio of adults : children $= 2 : 3$
So, total parts $= 2 + 3 = 5$
Adults $= \dfrac{2}{5} \times 100 = 40$
Children $= \dfrac{3}{5} \times 100 = 60$
Now use literacy data:
For adults:
Illiterate adults $= 40.1%$
So, literate adults $= 100% - 40.1% = 59.9%$
Literate adults $= 59.9%$ of $40$
$= \dfrac{59.9}{100} \times 40 = 23.96$
For children:
Literate children $= 85.1%$ of $60$
$= \dfrac{85.1}{100} \times 60 = 51.06$
Total literate population
$= 23.96 + 51.06 = 75.02$
Since total population is $100$,
Literate percentage $= 75.02% \approx 75%$.